Fifty-odd years ago, a young singer/dancer on the verge of breaking into the movies visited LIFE magazine’s Los Angeles bureau—and for once, the news hounds who worked there were speechless.

“Everybody was working on typewriters back then, so it was very noisy,” remembers the legendary editor Richard Stolley, who was L.A. bureau chief at the time. “I’m sitting in my office and suddenly it got quiet. All the typewriters stopped. I thought, ‘What the hell is going on?’ So I got up and I walked to the door. And what was happening? Ann-Margret was walking through the newsroom.”

Grey Villet—TIME & LIFE Pictures/Getty Images

Nineteen-year-old Ann-Margret belts out a tune during a screen test for the movie State Fair in 1961.

Here, Stolley and Ann-Margret herself reminisce about those long-ago days—days that remain distinct in both of their memories.

“That,” Stolley says of the picture at left, “is what you were wearing when you came in to the bureau.”

“It was a light blue, lambswool sweater,” Ann-Margret recalls, laughing. “That’s the only outfit I had at the time. The only one! Oh, dear.”

In the decades since that first encounter, Stolley served as the top editor of both LIFE and PEOPLE magazines, and that fresh-faced 19-year-old starlet did pretty well for herself, too: Ann-Margret, born Ann-Margret Olsson in Stockholm, became one of Hollywood’s sexiest, most vivacious stars, her energy and talent lighting up movies as varied as Bye Bye Birdie, Viva Las Vegas and Tommy. Through the years, the great journalist, now 84, and the marvelous actress, now 72, have remained dear friends.

For this LIFE.com feature, the two of them reminisced over photos made by Grey Villet (“Oh, I loved him,” she says of the late LIFE photographer) for the 1961 LIFE article that introduced Ann-Margret as a hot Hollywood prospect while she auditioned for a role in the film, State Fair.

Many of the photos in this gallery were not originally published in LIFE.

Below are some excerpts from their chat:

STOLLEY: How important was the LIFE story to your career?

ANN-MARGRET: It was incredibly important. I had not done anything—nobody knew me. I was amazed and shocked. What can I say? My parents were just beaming.

STOLLEY: The opening page on that story had a picture of you pointing, and the headline was “Who, Me? $10,000 a Week!” That was what we predicted would be your salary if you got the role in State Fair. How did you feel about $10,000 a week?

ANN-MARGRET: I had never heard of such money! That’s just sci-fi.

STOLLEY: How old were you when you came over to the States from Sweden?

ANN-MARGRET: Six years old. And it was my mother and I, because daddy had come to America [earlier] looking for work. That was during the war, and he thought it was much too dangerous for mother and I to cross the ocean. So five years later, my mother and I got on a huge ship and came to America. And neither one of us, of course, spoke English.

STOLLEY: There’s an unpublished picture here [the final image in this gallery] which is kind of fascinating. It’s you walking down the dusty back-lot street with a big, long shadow in front of you. The reason I like it is because it’s kind of a precursor, a forecast of the long shadow you were going to cast over Hollywood and the entertainment industry.

ANN-MARGRET: I had no idea at the time. Of anything.

STOLLEY: Nor did Grey, but he took a very prescient photograph. When I say something like that, what’s your reaction looking at this picture?

ANN-MARGRET: I’d never been to Los Angeles. Never. I wanted to be a …. [Trails off and chokes up] I can’t, I’m starting to cry!

STOLLEY: Don’t do that—I’m sorry.

ANN-MARGRET: When you guys [at LIFE.com] sent me all these photographs, what a rush. It all came back to me. It’s just . . . I’m so blessed.

On the screen test chronicled in Grey Villet’s photos: “Oh my gosh, I was so nervous. So nervous! I had the scene to do, the acting scene, and I had never done any acting. I mean, I had been a performer, singing and dancing, but I had not taken any acting lessons or anything.”

On George Burns, who gave Ann-Margret her first break as a singer and dancer in a Vegas show: When she auditioned for Burns, she said, she “wore the light blue lambswool sweater and the black stockings and little black one-inch shoes that I had worn all through the summer, because that’s all I had! And that’s the way Mr. Burns saw me. So on opening night, that’s what I wore. But then I searched all over the place for something that I thought would be really nice in Las Vegas, and it was more money than I had ever spent. It was an orangey-red velvet pantsuit, and pantsuits were just coming into style. And at dress rehearsal Mr. Burns saw this outfit, and he said [mimicking Burns’ famous rasp], ‘Where’s the sweater and pants that you wore on the audition—the tight sweater and the tight pants?’ And I said, ‘Well, I thought that this was really nice and that you’d like it.’ And he said, ‘People don’t want to only hear your voice, they want to see where it’s coming from!'” She laughs. “I never forgot that one.”

“I learned so much from him,” she reflects. “He loved to rehearse and I did, too. I would go over to his home and when we did a number, the singing and dancing, the final word was always [his wife] Gracie’s. She would come downstairs, she would sit on the couch, and if she liked it, we would do it. And if she didn’t, we’d have to fix it.”

“I sang for him on his hundredth birthday,” she recalls, fondly. “I sang, ‘I’ve Got a Crush on You.'”